Large-amplitude solitary water waves with discontinuous vorticity

Monday, July 17, 2017 - 2:00pm
111 MSB
Adelaide Akers (Advisor: Prof. Samuel Walsh)

Abstract:  We consider a two-dimensional body of water with constant density which lies below a vacuum.  The ocean bed is assumed to be impenetrable, while the boundary which separates the fluid and the vacuum is assumed to be a free boundary.  Under the assumption that the vorticity is only bounded and measurable, we prove that for any upstream velocity field, there exists a continuous curve of large-amplitude solitary wave solutions.  This is achieved via a local and global bifurcation construction of weak solutions to the elliptic equations which constitute the steady water wave problem.  We also show that such solutions possess a number of qualitative features; most significantly that each solitary wave is a symmetric, monotone wave of elevation.